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Unformatted text preview: Ø 6.003 Homework 13 Please do the following problems by Wednesday, May 12, 2010 . your answers: they will NOT be graded. Solutions will be posted. You need not submit Problems 1. Transformation Consider the following transformation from x ( t ) to y ( t ): × × × + x ( t ) y ( t ) p ( t ) cos( πt ) w 1 ( t ) w 2 ( t ) w 3 ( t ) where p ( t ) = ∞ Ø k = −∞ δ ( t − k ). Determine an expression for y ( t ) when x ( t ) = sin( πt/ 2) / ( πt ). 2. DT processing of CT signals ∞ Consider the following system for DT processing of CT signals: H 1 ( jω ) H 2 ( e j Ω ) H 3 ( jω ) uniform sampler sample-to- impulse x a ( t ) x b ( t ) x c [ n ] y d [ n ] y e ( t ) y f ( t ) where x c [ n ] = x b ( nT ) and y e ( t ) = y d [ n ] δ ( t − nT ) . n = −∞ The frequency responses H 1 ( jω ) and H 3 ( jω ) are given below. ω π 2 T − π 2 T 3 π 2 T − 3 π 2 T H 1 ( jω ) 1 ω π T − π T H 3 ( jω ) T Part a. Assume in this part that H 2 ( e j Ω ) = 1 for all frequencies...
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This note was uploaded on 12/14/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.
- Spring '11